Testing a Hypothesis about the Supernatural

[Angrboda]

Since the question was about the qualitative aspects of natural theology arguments as explanations and their similarity and substance on that axis, or lack thereof, you've talked around the question without actually engaging it.

Okay, this seems to be the point from your earliest post, so I will address that:

Indeed, theism as an explanation has much in common with what we know to be really bad explanations from pseudoscience and superstition, and almost nothing in common with what we know to be really good explanations from the physical sciences. So why should we think theism is a good explanation like those from science, rather than a really terrible explanation like those from pseudoscience and superstition?

This is one big category error. The article uses the term 'explanation' and then complain that the natural theology arguments don't meet the requirements of a scientific explanation (including what makes a for a good scientific explanation).  Inductive premises and the deductive conclusions of natural theology infer God as a fundamental feature of reality--not a scientific explanation. While support for some of the premises contain lots of science, the conclusion is always a metaphysical explanation. As further evidence of a category error, every scientific explanation always has a 'why?' on the far side of them, requiring a further explanation--and so on...forever. The natural theology metaphysical explanations: God, is a far better stopping point to an infinite regress of 'whys?' because, really, there is no sense to ask 'why' once you get to God. 

I think that in order to think the natural theology arguments and pseudoscience ('pseudo' means false) claims are similar, you have to 1) not really understand the natural theology arguments themselves and the support for each premise--which can fill chapters in a book and 2) already assume the natural theology conclusions are not true --which is question begging:

1. Natural theology claims are false
2. Therefore they are similar to pseudoscience ('false' science) claims

Well, let's start there, then. What do you mean, then, when you say that God is the best explanation for this or that fact of the natural world?